What is the Greatest Common Factor of 589 and 609?

Greatest common factor (GCF) of 589 and 609 is 1.

GCF(589,609) = 1

We will now calculate the prime factors of 589 and 609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 589 and 609.

How to find the GCF of 589 and 609?

We will first find the prime factorization of 589 and 609. After we will calculate the factors of 589 and 609 and find the biggest common factor number .

Step-1: Prime Factorization of 589

Prime factors of 589 are 19, 31. Prime factorization of 589 in exponential form is:

589 = 19¹ × 31¹

Step-2: Prime Factorization of 609

Prime factors of 609 are 3, 7, 29. Prime factorization of 609 in exponential form is:

609 = 3¹ × 7¹ × 29¹

Step-3: Factors of 589

List of positive integer factors of 589 that divides 589 without a remainder.

1, 19, 31

Step-4: Factors of 609

List of positive integer factors of 609 that divides 589 without a remainder.

1, 3, 7, 21, 29, 87, 203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 589 and 609. The biggest common factor number is the GCF number.
So the greatest common factor 589 and 609 is 1.

Also check out the Least Common Multiple of 589 and 609